Stability of contact discontinuity for steady Euler system in infinite duct

Abstract

In this paper, we prove stability of contact discontinuities for full Euler system. We fix a flat duct of infinite length in with width W (0) and consider two uniform subsonic flow with different horizontal velocity in divided by a flat contact discontinuity . And, we slightly perturb the boundary of so that the width of the perturbed duct converges to for at for some . Then, we prove that if the asymptotic state at left far field is given by , and if the perturbation of boundary of and is sufficiently small, then there exists unique asymptotic state with a flat contact discontinuity at right far field() and unique weak solution of the Euler system so that U consists of two subsonic flow with a contact discontinuity in between, and that U converges to and at and respectively. For that purpose, we establish piecewise C (1) estimate across a contact discontinuity of a weak solution to Euler system depending on the perturbation of and .